A Note on Toroidal Compactifications of the Type I Superstring and Other Superstring Vacuum Configurations with 16 Supercharges

TL;DR

This paper explores various disconnected components of superstring vacua with 16 supercharges, using BPS un-orientifolds and dualities to relate different string theories and compactifications.

Contribution

It introduces a framework for understanding disconnected superstring vacua via BPS un-orientifolds and dualities, linking type I, heterotic, type II, and M-theory compactifications.

Findings

Disconnected components correspond to BPS un-orientifolds with quantized NS-NS flux.

Type I vacua without open strings relate to type II (4,0) superstrings without D-branes.

U-duality connects various superstring vacua below D=6.

Abstract

We show that various disconnected components of the moduli space of superstring vacua with 16 supercharges admit a rationale in terms of BPS un-orientifolds, i.e. type I toroidal compactifications with constant non-vanishing but quantized vacuum expectation values of the NS-NS antisymmetric tensor. These include various heterotic vacua with reduced rank, known as CHL strings, and their dual type II (2,2) superstrings below D=6. Type I vacua without open strings allow for an interpretation of several disconnected components with N_V=10-D. An adiabatic argument relates these unconventional type I superstrings to type II (4,0) superstrings without D-branes. The latter are connected by U-duality below D=6 to type II (2,2) superstrings. We also comment on the relation between some of these vacua and compactifications of the putative M-theory on unorientable manifolds as well as F-theory vacua.